Problem: Evaluate the definite integral. $\int^{25}_{0}\left(-12\sqrt{x}\right)\,dx = $
Explanation: First, use the power rule: $\begin{aligned}\int^{25}_{0}\left(-12\sqrt{x}\right)\,dx ~&=~\int^{25}_{0}\left(-12x^{\frac12}\right)\,dx \\&=(-8x^\frac32)\Bigg|^{25}_{{0}}\end{aligned}$ Second, plug in the limits of integration: $(-8\cdot{25}^{\frac32})-(-8\cdot{0}^{\frac32}) = -1000+0 = -1000$. The answer: $\int^{36}_{25}\left(-12\sqrt{x}\right)\,dx ~=~-1000$